Question

Identifying a Sequence of Transformations
On a coordinate plane, triangle L M N has points (2, 1), (1, 1), (1, 3). Triangle L prime M prime N prime has points (negative 4, negative 4), (negative 3, negative 4), (negative 3, negative 2).

Which sequence of transformations produces
TriangleL'M'N' from TriangleLMN?
a translation 5 units down and 2 units to the right followed by a reflection across the y-axis
a reflection across the y-axis followed by a translation 5 units down and 2 units right
a translation 5 units down and 2 units to the left followed by a reflection across the y-axis
no sequence of transformations

Answer 1

Answer: a translation 5 units down and 2 units to the right followed by a reflection across the y-axis.

Check: translate (x,y) by ( +2, −5 ) → (x+2, y−5). Reflect across the y-axis → (−(x+2), y−5) = (−x−2, y−5).

Apply to each vertex:
- L(2,1): (−2−2, 1−5) = (−4, −4) = L'
- M(1,1): (−1−2, 1−5) = (−3, −4) = M'
- N(1,3): (−1−2, 3−5) = (−3, −2) = N'

So option A is correct.